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Sci. Signal., 27 September 2011
Vol. 4, Issue 192, p. tr9
[DOI: 10.1126/scisignal.2001983]


Biomedical Model Fitting and Error Analysis

Kevin D. Costa1*, Steven H. Kleinstein2,3, and Uri Hershberg4

1 Department of Medicine (Cardiology), Mount Sinai School of Medicine, New York, NY 10029, USA.
2 Department of Pathology, Yale School of Medicine, New Haven, CT 06520, USA.
3 Interdepartmental Program in Computational Biology and Bioinformatics, Yale University, New Haven, CT 06520, USA.
4 School of Biomedical Engineering, Science and Health Systems, Drexel University, Philadelphia, PA 19104, USA.

Abstract: This Teaching Resource introduces students to curve fitting and error analysis; it is the second of two lectures on developing mathematical models of biomedical systems. The first focused on identifying, extracting, and converting required constants—such as kinetic rate constants—from experimental literature. To understand how such constants are determined from experimental data, this lecture introduces the principles and practice of fitting a mathematical model to a series of measurements. We emphasize using nonlinear models for fitting nonlinear data, avoiding problems associated with linearization schemes that can distort and misrepresent the data. To help ensure proper interpretation of model parameters estimated by inverse modeling, we describe a rigorous six-step process: (i) selecting an appropriate mathematical model; (ii) defining a "figure-of-merit" function that quantifies the error between the model and data; (iii) adjusting model parameters to get a "best fit" to the data; (iv) examining the "goodness of fit" to the data; (v) determining whether a much better fit is possible; and (vi) evaluating the accuracy of the best-fit parameter values. Implementation of the computational methods is based on MATLAB, with example programs provided that can be modified for particular applications. The problem set allows students to use these programs to develop practical experience with the inverse-modeling process in the context of determining the rates of cell proliferation and death for B lymphocytes using data from BrdU-labeling experiments.

* Corresponding author. E-mail, kevin.costa{at}

Citation: K. D. Costa, S. H. Kleinstein, U. Hershberg, Biomedical Model Fitting and Error Analysis. Sci. Signal. 4, tr9 (2011).

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